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## Evaluating Exponents

#### Introduction

Exponents are a way of writing that a number is being multiplied by itself and telling you how many times to do it.

For example, if we multiply 3 x 3, we can write $3^{2}$. The $^{2}$ tells us that you have 2 threes that you are multiplying together. If we were to have $3^{3}$ then we would have three threes to multiply together which would be 3 x 3 x 3.

## Lesson

To evaluate an exponent you need to break it up into its parts. The first number tells you what you are multiplying, and the exponent tells you how many of these numbers to multiply together. For example, in the expression:

$5^{2}$

The 5 is the number to be multiplied, and the $^{2}$ tells us that we need to multiply together two fives, so

$5^{2}$ = 5 x 5 = 25

In the expression:

$2^{6}$

The 2 is the number to be multiplied, and we need to do it 6 times:

$2^{6}$ = 2 x 2 x 2 x 2 x 2 x 2 = 64

### Some rules to remember:

Any exponent of 0 is still zero.

$0^{3}$ = 0 x 0 x 0 = 0

Any exponent of 1 is still 1.

$1^{5}$ = 1 x 1 x 1 x 1 x 1 = 1

Any number to the exponent of 0 = 1

$5^{0}$ = 1

$18^{0}$ = 1

$2305^{0}$ = 1

## Examples

#### Evaluating Exponents (Example #1)

$\left(\dfrac{1}{3}\right)^{3}$
$\dfrac{1}{3} * \dfrac{1}{3} * \dfrac{1}{3}$
$\left(\dfrac{1}{3}\right)^{3} = \dfrac{1}{27}$

#### Evaluating Exponents (Example #2)

$\left(\dfrac{1}{4}\right)^{-2}$
KaTeX can only parse string typed expression
$\left(\dfrac{1}{4}\right)^{-2} = 16$

#### Evaluating Exponents (Example #3)

$\left(\dfrac{2}{5}\right)^{0}$
Any number raised to the zero power is one
$\left(\dfrac{2}{5}\right)^{0} = 1$

#### Evaluating Exponents (Example #4)

$3^{4}$
$3 * 3 * 3 * 3$
$3^{4} = 81$

#### Evaluating Exponents (Example #5)

$\left(-3\right)^{-4}$
KaTeX can only parse string typed expression
$\left(-3\right)^{-4} = \dfrac{1}{81}$

#### Evaluating Exponents (Example #6)

$5^{-3}$
KaTeX can only parse string typed expression
$5^{-3} = \dfrac{1}{125}$